ON THE CO-DEPENDENCE OF TIME DILATION, SUPERLUMINAL VELOCITIES, AND RELATIVISTIC MASS
Vertner Vergon

It is time to set the record straight, to interpret correctly the misinterpretations of Einstein. The areas that need clarification are Time Dilation, Relativistic Mass, and c as a limit (Superluminal Velocities). These three are all tied together, one dependent upon the other.

Not to discuss whether UFOs really exist but rather if there were intelligent life elsewhere in the universe -- and they had a high technology -- could they reach us considering the vast distances, the limiting speed of light, and the time it would take for voyagers to transit? Is there a velocity/time barrier surrounding us that forever places us in isolation? Fortunately (or maybe unfortunately) the answer is no for superluminal velocities are possible and the only limit placed on interstellar travel is the technology of transit, i.e., the technology of attainable velocity.

As a consequence, this dissertation will deal firstly with the existence of superluminal velocities. To do this we will summarize the Dual Velocity Theory of Relativity. It seems everybody agrees *observed* longitudinal length in an observed frame decreases with an increase in relative velocity.

Postulate 1: Longitudinal length and "distance" are the same thing as longitudinal length is also a distance.

Postulate 2: Velocity is distance per unit time.

Conclusion: Since longitudinal length reduces with an increase in velocity, then *observed* velocity reduces with an increase in velocity of the moving frame. Restated: The velocity of the moving frame is greater than the observed velocity. Thus we have two velocities, the observed velocity -- and the true velocity of the moving frame. The two velocities are Lorentz variant. That is true velocity times the Lorentz transform equals the observed velocity.

Where V is the velocity of the moving frame, v the observed velocity, and R the Lorentz transform ---

√ ( 1- v²/c²) , V x R = v

Thus there are two velocities, that which is extant -- and that which is observed. It will be found that as V goes to infinity, v goes to c. Therefore we conclude that superluminal velocities exist. We also conclude that in p = mv/R, the R applies to v not to m. So there is no such thing as relativistic mass. The mass is invariable and v is the observation of V that goes to infinity as R goes to zero.

Scenario 1

If you pursue a beam of light, your velocity has to be relative to the emitter. As you gain in velocity the frequency reduces. At c it is zero. No "spatial oscillation". Also, at c, the energy of the photon is zero -- and the momentum is zero. Zero frequency, zero energy, zero momentum = there is nothing to observe. But how can that be? The photon must have consisted of something. The only conclusion is that what you behold are a static electric and static magnetic field. They are at rest to you and have no energy, momentum or frequency.

There is a problem with our posit. The speed of light is c to all frames. We state you pursue a beam of light. Forgotten is that that beam of light will *always* precede you at c -- thus you can never attain a velocity equal to the photon. So even as the frequency goes to zero (and the energy and momentum too) the beam is preceding you at c.

Does that mean the velocity of the photon is 2c? Consider the spatial contraction aspect. At c *all* the space up front is apparently contracted to zero. That means the photon is everywhere up front at once. That is why time in the photon's frame is considered stopped. It can cover any distance with no lapse in time. With a little cogitation one realizes that fits the description of infinite velocity.

We should not be so enamored about the accuracy of mathematics. Whereas the procedures and operations may be more or less accurate, the failings come in the interpretations of the results.

In his clock gedanken experiment, Einstein saw his moving clock was "behind" (his word) the at rest clock and concluded that the moving clock ran slower. Wrong.

Correct interpretation: The moving clock traveled faster than measured -- and therefore made its transit in less time than experienced by the inertial clock. Therefore, with both clocks keeping the same rate, the moving clock makes its transit in *less time*. Thus we see the moving clock keeping proper time but being behind the inertial clock at the end of its journey. There is no slowing of the clock. Thus we see time dilation as proposed by Einstein does not exist. (Nor does the Twin Paradox.)

Einstein's math showed that as a body approached c, its energy requirements, approached infinity as did its momentum. His conclusion: This was due to an increase in inertial mass -- thus the bugaboo of relativistic mass was born. His math also showed that as a body approached c, its transit time of a longitudinal distance approached zero. The transit time approaching zero was offered as time dilation.

Both wrong. There was given no cause and effect reason for the mass increase and time dilation. Time dilation was already indicated as not existing due to the fact it created a reductio ad absurdom known as the Twin Paradox. Such a condition is a wildly waving flag that something is wrong with a theory and that it has to be reworked. Such was not done.

The longitudinal length of a moving system *appears* to contract due to the measurement being made by the use of light which has an invariant velocity of c. Einstein could have concluded that as the apparent length of a moving system contracted, so would the velocity itself undergo a foreshortening. This would result in the following: As the velocity of a body approached infinity, the foreshortened *measured* velocity would approach c -- the maximum velocity of the measuring tool.

As a matter of fact, if one does the arithmetic, they will find that the energy requirements, the momentum and the transit time of a body do not fit the relative velocity but DO fit the corresponding actual (Newtonian) velocity. Thus we see the parameters of the Newtonian velocity in the company of the measured corresponding relative velocity.

Then there is the general (mis)interpretation of the energy-momentum 4 vector equation. This equation is nothing more or less than the combination of Einstein's equations for the energy and momentum of moving *bodies* -- "bodies", not radiation. The general interpretation of the equation, E² = (mc²)² + (pc)² is as follows: "If we set the m in the right hand first term to zero, then we get E = pc which we know is true. This shows that the mass of the photon is zero."

Wrong.

The first term is the square of mc². In case one forgets, mc² is REST energy -- and the m is REST mass. Do we agree that the REST mass of the photon is zero? Of course. A photon brought to rest (by absorption) is no longer a photon -- so its REST mass is zero. The second RH term is pc, the energy of a photon IN FLIGHT. The p is momentum – which we know the photon in flight has.

Every equation for momentum contains MASS and motion. Therefore E = pc states that the photon in flight has mass. When faced with that fact, the poor souls who misinterpreted the equation try to maintain their position by declaring a new physics whereby there exists momentum with no mass. The problem is, they cannot substantiate that.

"When you can measure what you are speaking about and express it in numbers, you know something about it." Lord Kelvin (1824-1907)

Einstein's thesis is entitled "On the Electrodynamics of Moving Bodies". So what does that actually mean? It is on the interaction of light and moving systems. It might well be titled "The observation of fast moving systems". Note, the operational word is OBSERVATION.

A rod in the system does not contract (along the line of motion) -- a clock does

not change the rate of its ticking -- the mass of any object in the system does not change -- -- everything in the system stays the same, it is the OBSERVATION that is distorted. In short, there is an ABERRATION due to the fact that light -- the message carrier -- travels at an invariable velocity (c). Observe the fact that light creates two aberrations, (1) the aberration caused by refraction, and (2) the aberration caused by the constancy of velocity.

In the first instance, the fish in the river pool is not where it appears to be -- and in the second the condition of items in the moving system are not undergoing the changes they appear to. If one keeps that in mind they will avoid a lot of wrong conclusions.

One of the errors assumed from the theory is that c is the limiting velocity of the universe. The correct conclusion is that c is the limiting OBSERVED velocity in the universe -- because that is the limit of the message carrier. The message carrier can be "tricked" into revealing superluminal velocities. Here is one way.

Assume two points one light year apart -- A and B. Assume that there is an observer equidistant from both points. Next, we have an object expend sufficient energy to attain a velocity of 12 c. Thus it will transit the 12 light months in one month. The observer, being equidistant from both A and B can disregard the transit time for light to carry the messages of departure and arrival. He will receive these signals one month apart. Thus he will measure a superluminal velocity of 12c.

However, an observer at A will measure the velocity as given by Einstein – for A, B is along the x axis. So we see there are two velocities -- the velocity extant, and the velocity observed. (Just as there is the actual location of the fish -- and where it appears to be.) We shall call the Einstein velocity the relative velocity -- and the superluminal velocity Newtonian (because that's what it is.)

In the present example the relative velocity is .9965458 c and the Lorentz factor is .08304548.

Now if one calculates the kinetic energy and relative momentum for unit mass they will discover that it is the same for 12c using Newtonian equations. In other words the parameters for the Newtonian velocity are to be found accompanying the relativistic velocity. There is one caveat, however. The equation E = mv²/2 is only good for low velocities. The correct equation for all velocities is E mv²/R + R² which degenerates to mv²/2 at low velocities. It will be found that this is exactly equal to Einstein’s E = (1/R -1)mc².

Examining this dual velocity further, we see it dissolves the Twin Paradox. The Earth twin measures the relativistic velocity. The Astronaut twin experiences the Newtonian velocity. Since the Newtonian velocity is faster than the relativistic , the astronaut accomplishes it in less time than that observed on Earth by the Earth twin.

There is a saying, "If he fell in a sewer, he'd come up with a gold coin. Einstein (whom I admire) was such an individual. He was 25 when he wrote his theory, 26 when it was published. His concept was impeccable, his mathematics correct. However, he fumbled in the interpretation of the mathematical results. This created a mystique haunting a theory that was basically correct but that played havoc with our intuitive concept of the universe -- one that was neatly categorized by Newton.

Rather than dealing only with the relativity of moving bodies he brought in the electrodynamics also -- to some brilliant conclusions. Had he interpreted his mathematics correctly, what would have transpired was the creation of a theory that neatly packaged various concepts of the *principle* of relativity that had been around for a while. People would say, "That's nice." and put it on the shelf along with other accepted theories of how our universe works and he would have taken his place in equal standing alongside many other brilliant physicists.

But Einstein misfired. He made interpretive errors that made his theory – and him -- super famous because the concepts were bizarre and resolution elusive. Perhaps the main one was the interpretation that led to the Twin Paradox -- the concept of time dilation. How many millions of hours have been spent discussing that? He discusses two identical clocks, one of which goes on a journey and returns to the stationary one. He notes that the clock that journeyed was "behind" (his word) the stationary clock, i.e., showed less time.